v=5; t=3; L=5; g=9.81;
tolerance = 1e-5;
rel_error = 1;

%initial guesses
xl = 0.01;
xu = 10;

fxu = v/sqrt(2*g*xu) - tanh (t/(2*L)*sqrt(2*g*xu));
fxl = v/sqrt(2*g*xl) - tanh (t/(2*L)*sqrt(2*g*xl));
xr = xu - fxu*(xl-xu)/(fxl-fxu);
fxr = v/sqrt(2*g*xr) - tanh (t/(2*L)*sqrt(2*g*xr));

while (rel_error > tolerance)
if (fxl*fxr<0)
	xrold = xr
	xu = xr;
	fxu = v/sqrt(2*g*xu) - tanh (t/(2*L)*sqrt(2*g*xu));
	xr = xu - fxu*(xl-xu)/(fxl-fxu);
	fxr = v/sqrt(2*g*xr) - tanh (t/(2*L)*sqrt(2*g*xr));
	rel_error =abs((xr - xrold)/xr)*100;
	
else
	xrold = xr
	xl = xr;
	fxl = v/sqrt(2*g*xl) - tanh (t/(2*L)*sqrt(2*g*xl));
	xr = xu - fxu*(xl-xu)/(fxl-fxu);
	fxr = v/sqrt(2*g*xr) - tanh (t/(2*L)*sqrt(2*g*xr));
	rel_error =abs((xr - xrold)/xr)*100;

end
end
root = xr